Session R27: Flow Instability: Boundary Layers and Transition to Turbulence II

Stability characteristics of the boundary layer developing on a flat plate with spanwise sinusoidal corrugations

In low disturbance environments boundary layer transition is tipically driven by Tollmien-Schlichting (TS) waves. In passive controls aimed at transition delay, minimal geometric modifications are introduced to attenuate TS waves. Following the strategy called "spanwise mean velocity gradient" (SVG, see [1]), TS waves can be attenuated by inducing appropriate spanwise modulations of the streamwise velocity. A number of successful examples of SVG have been documented in the literature, and most of these are related to the use of miniature vortex generators (MVGs, see [2]).

In the present investigation the SVG method is implemented by small-amplitude spanwise sinusoidal corrugations of the wall of a nominally flat plate. Compared to localised controls, such as those based on MVGs, the strategy proposed here has several advantages, i.e. it is less intrusive, easier to implement in practice, and and has a more prolonged effect on the flow in the streamwise direction. This specific control has been proposed and experimentally investigated by Prof. J.H.M. Fransson and co-workers at KTH Mechanics of Stockholm [personal communication]. 

The characteristics of flow fields computed by dedicated simulations are discussed here for a wide range of free parameters of the geometry. In addition, the effect of the control on the spatial stability curves is shown and the most effective geometries for influencing transition are identified.

 [1] Shahinfar, S., Fransson, J. H. M., Sattarzadeh, S. S., Talamelli, A., 2013, J. Fluid Mech., 733, 1--32.

 [2] Shahinfar, S., Sattarzadeh, S. S., Fransson, J. H. M., Talamelli, A., 2012, Phys. Rev. Lett. 109, 074501.   

Numerical Investigation of Fluid-Ablation Interactions in a Mach 5.3 Boundary Layer

Performing fully-coupled simulations of a transitional boundary layer flowing over an ablative

material is still a difficult task. Most ablation problems of interest evolve over a time scale

of O(10) seconds. With explicit time integration, a tractable direct numerical simulation

(DNS) solution of the fluid can be obtained for only O(10−3) seconds of physical time. This

work attempts to use tight coupling between the two sets of physics in order to simulate

boundary layer transition to turbulence over an ablating flat plate. Of chief interest is the

concurrent influences of unsteady fluid motion on the material response and the material

response on the unsteady fluid motion. Also to be investigated is the legitimacy of various

techniques to maintain tight solver couplings while accelerating the ablation process.

This work has been funded by a CAREER grant by the National Science Foundation under

award CBET-2146100 with Dr. R. Joslin as Program Manager. The authors would also

like to thank Dr. J. McQuaid and Dr. A. Zibitsker for their development of the fluid and

material response codes used in this work, respectively.   

Effects of transpiration fluid properties on Boundary Layer Instability Mechanisms

The management of intense thermal loads encountered by hypersonic vehicles operating in the atmosphere

can be effectively alleviated by utilizing transpiration cooling, which involves the injection of cold fluids at

the vehicle’s surface. However, injection can substantially impact flow stability and potentially

induce a premature transition to turbulence. The primary objective of this study is to comprehensively

understand the mechanisms responsible for the destabilization of the flow for different injection fluids. To

assess the influence of injection gas properties on the stability of high-enthalpy boundary layer flows, air

and CO2 injections are being considered. Both fluids are introduced at the same mass flux, resulting in

a comparable reduction in heat flux. Disturbance energy budget analysis is used to explain the relevant physical mechanisms. Furthermore, Bi-Orthogonal Decomposition is used to differentiate the different contributions from eigenmode spectrum.   

Direct numerical simulation of H-type transition in stratified horizontal boundary layers

Thermal stratification in boundary layers occurs in many natural phenomena and industrial applications, such as atmospheric boundary layers and heat exchangers. In these cases, the stratification can significantly affect hydrodynamic stability. While buoyancy effects on fully developed turbulence have been widely investigated, laminar-to-turbulent transition of horizontal boundary layers is mostly unexplored. In this study, we conduct direct numerical simulations of H-type breakdown in flat-plate boundary layers with weak wall-heating (T_w/T_∞=1.05) at a Mach number of 0.2. We examine a range of Richardson numbers, based on the inlet boundary-layer thickness, wall density, and gravitational acceleration, from 0.01 to -0.02. First, primary and secondary perturbation growth rates in stably- and unstably-stratified configurations are analyzed. Buoyancy forces either decrease or increase primary and secondary instability growth rates and thus either delay or promote the transition to turbulence. We propose a scaling law as a function of the Richardson number that successfully predicts the primary and secondary growth rates. The physical mechanisms of non-neutral stratification on the instability growth are then investigated based on the vorticity fluctuation equation. As for the primary instability, the buoyancy term exhibits a peak near the critical layer, where it is in phase with the spanwise vorticity fluctuation.   

Bispectral analysis of nonlinear dynamics and its connection to skin friction in heated/cooled transonic boundary layer transition

We study the impacts of wall heating/cooling on the nonlinear dynamics in the boundary layer transition and its relation to skin friction. Direct numerical simulations (DNS) of the transition over a 10%-heated/cooled flat plate are conducted. The transition is initiated by a tiny planer wave, a counterpart of the Tollmien-Schlichting (TS) wave in an incompressible flow, and a subharmonic oblique wave (OW), which can cause the H-type transition. The DNS results show a distinct difference in the streamwise growth of skin friction (Cf) between the adiabatic/heated and cooled cases. For the former cases, there is a monotonically steep rise in Cf in the nonlinear (transitional) region, whereas the cooled case shows a two-stage rise: gradual at first, then steep. We identify that this difference results from suppressing the TS mode's linear growth with wall cooling; its amplitude is up to about ten times smaller than the heated case. We quantify the degree of nonlinear interaction of modes using the bispectrum computed by bispectral mode decomposition (BMD). The bispectrum reveals that the TS mode plays a marginal role in the nonlinear dynamics for the cooled case in contrast to the adiabatic/heated cases, while the OW mode and steady stream (ST) mode nonlinearly generated by OW mode play an essential role. Moreover, the BMD suggests that the ST mode's self-interaction is relevant to the early stage with the gradual rise in Cf while the OW mode's self-interaction to the late stage with the rapid rise in Cf.   

Reynolds number effect on flow structure dominance in transitional boundary layers

Understanding the dominant flow structures that govern the flow physics of transitional boundary layers subject to external forcing is crucial for designing feedback controllers in active flow control applications. Herein, we study the impact of linear and nonlinear mechanisms on the resulting flow structures due to external excitation for a wide range of Reynolds numbers and for three canonical base flows: Couette flow, plane Poiseuille flow, and Blasius flow. To preserve the nonlinearity of the Navier–Stokes equations, we use a structured input-output analysis, where two different uncertainty structures were implemented based on studies of J. Fluid Mech. vol. 927, A25, and Int J Robust Nonlinear Control vol. 34(7): 4881-4897. For each flow case, we track the variation of several modes of interest that have been identified as dominant via linear and nonlinear input-output approaches. We show that streak modes that are predicted via linear input-output analysis lose their dominance when using structured input-output analysis, where for low Reynolds numbers, more modes appear to be similar in strength. We find that amplification trends of these modes vary with the Reynolds number increase, leading to an interchange of mode dominance for different Reynolds numbers.   

The effect of waveform shape, Womersley number, and pulsation amplitude on transitional pulsatile pipe flow: a 4D PTV study

Previous studies have shown that pulsatile pipe flow mimics steady flow at high Womersley numbers (Wo>10), highlighting that a “critical Womersley number” likely exists, beyond which on transition is no longer influenced by Womersley number-specific effects. However, inconsistencies regarding the specific effects of Womersley number on transitional pulsatile pipe flow have been reported across literature indicating that underlying factors likely have yet to be completely studied. In this study, we use volumetric particle tracking velocimetry (PTV) to investigate the isolated effects of relevant parameters like waveform shape and pulsation amplitude. Additionally, we study their combined effects with changing Womersley number across laminar, transitional, and turbulent flow regimes. We compute turbulent kinetic energy, turbulence intensity, and phase lag. Through this analysis, we evaluate the underlying trends and interactive relations between waveform shape, Womersley number, and pulsation amplitude. This work will provide a wholistic picture of how these axial flow factors affect transition in an effort to resolve the conflicting results across the literature.    

Discontinuous transition to shear flow turbulence

The transition to turbulence in wall bounded shear flows is characterized by the co-existence of turbulent and laminar regions. As discussed in a variety of recent studies this transition type corresponds to a continuous phase transition and falls into the universality class of directed percolation. We will demonstrate here that the nature of this transition fundamentally changes in the presence of body forces. We present experimental and numerical studies of more complex situations such as vertically heated pipes, curved pipes and MHD channel flow. In all these situations, with increasing amplitude of the body force, spatio-temporal intermittency is suppressed, and eventually the familiar flow structures such as turbulent puffs, slugs or stripes, are fully suppressed. Instead of continuous the phase transition becomes discontinuous and hence the flow transitions directly from laminar to fully turbulent as the Reynolds number is increased. As shown the mechanism responsible for this drastic change is the suppression of spatial coupling and the elimination of energy transfer between laminar and turbulent regions.